ON THE WEAK-TENACITY OF GRAPHS

Connectivity has been used in the past to describe the stability of graphs. If two graphs have the same connectivity, then it dose not distinguish between these graphs. That is, the Connectivity is not a good measure of graph stability. The we need other same Connectivity and the orther of the largest components of these graphs are not equal. Hence, we say that these graphs must be different in respect to stability and so we can define a new measore which distinguishes these graphs. In this paper, the Weak-Tenacity of graphs G is introduced as a new measure of stability in this sense and it is defined as where me(G-S) denotes the number of edges of the largest component of G-S.

Keywords:

vulnerability , connectivity , tenacity